Finite Group Databasebeta

← #34080365

Subgroups — #34080365

Order 19328.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752840C211yesmaximal, characteristic, complemented
2#23752817C211yesmaximal, characteristic
3#23752621C211yesmaximal, characteristic, complemented
4#23752614C211yesmaximal, characteristic, complemented
5#23752577C211yesmaximal, characteristic, complemented
6#23752559C211yesmaximal, characteristic, complemented
7#23752537C211yesmaximal, characteristic, complemented
8#23752537C211yesmaximal, characteristic, complemented
9#23752531C211yesmaximal, characteristic, complemented
10#23752526C211yesmaximal, characteristic, complemented
11#23752513C211yesmaximal, characteristic, complemented
12#23752513C211yesmaximal, characteristic, complemented
13#23752503C211yesmaximal, characteristic, complemented
14#23752493C211yesmaximal, characteristic, complemented
15#433×C151C211yesmaximal, characteristic, complemented
16#18012739C2211yescharacteristic
17#18012739C2211yescharacteristic
18#18012738—21no—
19#18012736C2211yescharacteristic
20#18012731C2211yescharacteristic
21#18012731C2211yescharacteristic
22#18012731C2211yescharacteristic
23#18012730—21no—
24#18012724—21no—
25#18012724—21no—
26#18012716—21no—
27#18012716—21no—
28#18012713C2211yescharacteristic
29#18012713C2211yescharacteristic
30#18012712—21no—
31#18012712—21no—
32C4×D604C2211yescharacteristic
33C4×D604C2211yescharacteristic
34#18012698C2211yescharacteristic
35C2×C4⋊Dic151C2211yescharacteristic
36#18012673C2211yescharacteristic
37#18012673C2211yescharacteristic
38#18012673C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012671C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012671C2211yescharacteristic
43#18012671C2211yescharacteristic
44#18012661C2211yescharacteristic
45#18012661C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic
51#18012661C2211yescharacteristic
52#117×C151C2211yescharacteristic
53C4⋊C8×C151C2211yescharacteristic
54C4⋊C8×C151C2211yescharacteristic
55C22⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57#97×C151C2211yescharacteristic
58C4×C8×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302—21no—
61C2×D604—21no—
62C2×D604—21no—
63C2×D604C2311yescharacteristic
64C2×D604C2311yescharacteristic
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C22×Dic151—21no—
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C4⋊Dic151—21no—
71C4⋊Dic151—21no—
72C4⋊Dic151—21no—
73C4⋊Dic151C2311yescharacteristic
74C4⋊Dic151C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4—21no—
84Dic151⋊C4—21no—
85C22⋊Dic151—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90C4×Dic151—21no—
91C22×C4×C151C2311yescharacteristic
92C2×C8×C151C2311yescharacteristic
93C2×C8×C151C2311yescharacteristic
94C2×C8×C151C2311yescharacteristic
95C2×C8×C151C2311yescharacteristic
96C4⋊C4×C151D411yescharacteristic
97C4⋊C4×C151D411yescharacteristic
98C22⋊C4×C151D411yescharacteristic
99C22⋊C4×C151D411yescharacteristic
100C42×C151C2311yescharacteristic
101C42×C151C2311yescharacteristic
102C22×D151—21no—
103C22×D151—21no—
104Dic302—81no—
105Dic302—81no—
106D604—21no—
107D604—21no—
108D604—21no—
109D604—21no—
110D604—81no—
111D604—81no—
112C22⋊D151—81no—
113C22⋊D151—81no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—81no—
121C4×D151—81no—
122C4×D151—81no—
123C23×C151C2×D411yescharacteristic
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151C2×D411yescharacteristic
127C2×C4×C151C2×D411yescharacteristic
128C2×C4×C151C2×D411yescharacteristic
129C2×C4×C151C2×D411yescharacteristic
130C2×C4×C151C2×D411yescharacteristic
131C2×C4×C151C2411yescharacteristic
132C8×C151—21no—
133C8×C151—21no—
134C8×C151—21no—
135C8×C151—21no—
136C22×C151—21no—
137C22×C151—21no—
138C22×C151—21no—
139C22×C151C22×D411yescharacteristic
140C2×D151—41no—
141C2×D151—41no—
142C2×D151—41no—
143C2×D151—41no—
144C2×D151—41no—
145C2×D151—41no—
146C4×C151—21no—
147C4×C151—21no—
148C4×C151—21no—
149C4×C151—21no—
150C4×C151—21no—
151C4×C1512−1+411yescharacteristic
152C4×C1512−1+411yescharacteristic
153Dic151—41no—
154Dic151—41no—
155Dic151—41no—
156Dic151—41no—
157Dic151—41no—
158Dic151—41no—
159C2×C151—41no—
160C2×C151#53611yescharacteristic
161C2×C151#57611yescharacteristic
162C2×C151#57711yescharacteristic
163D151—81no—
164D151—81no—
165C151#324111yescharacteristic, complemented, Sylow
166#3241—1511nomaximal, Sylow
167#544—1511no—
168#540—1511no—
169#501—1511no—
170#499—1511no—
171#490—1511no—
172#486—1511no—
173#482—1511no—
174#482—1511no—
175#481—1511no—
176#480—1511no—
177#478—1511no—
178#478—1511no—
179#476—1511no—
180#474—1511no—
181#433D15111yescharacteristic, complemented
182C4⋊Q8—3021no—
183C4⋊Q8—1511no—
184C4⋊Q8—1511no—
185#127—1511no—
186#125—3021no—
187#125—1511no—
188#125—1511no—
189#125—1511no—
190#123—3021no—
191#123—3021no—
192C22⋊Q8—3021no—
193C22⋊Q8—3021no—
194#121—3021no—
195#121—3021no—
196#121—1511no—
197#121—1511no—
198C4×D4—1511no—
199C4×D4—1511no—
200#117—1511no—
201#117C2×D15111yescharacteristic
202C2×C4⋊C4—1511no—
203#107—1511no—
204#107—1511no—
205#107—1511no—
206#107—1511no—
207#106—1511no—
208#106—1511no—
209#106—1511no—
210#106—1511no—
211C4⋊C8C2×D15111yescharacteristic
212C4⋊C8C2×D15111yescharacteristic
213#102—1511no—
214#102—1511no—
215#102—1511no—
216#102—1511no—
217#102—1511no—
218#102—1511no—
219#102—1511no—
220#102—1511no—
221C22⋊C8C2×D15111yescharacteristic
222C22⋊C8C2×D15111yescharacteristic
223#97C2×D15111yescharacteristic
224C4×C8C2×D15111yescharacteristic
225C2×Q8—3021no—
226C2×Q8—3021no—
227C2×D4—3021no—
228C2×D4—3021no—
229C2×D4—3021no—
230C2×D4—3021no—
231C2×D4—1511no—
232C2×D4—1511no—
233C22×C4—3021no—
234C22×C4—3021no—
235C22×C4—3021no—
236C22×C4C22×D15111yescharacteristic
237C2×C8C22×D15111yescharacteristic
238C2×C8C22×D15111yescharacteristic
239C2×C8C22×D15111yescharacteristic
240C2×C8C22×D15111yescharacteristic
241C4⋊C4—3021no—
242C4⋊C4—3021no—
243C4⋊C4—3021no—
244C4⋊C4—3021no—
245C4⋊C4—3021no—
246C4⋊C4—3021no—
247C4⋊C4—3021no—
248C4⋊C4—3021no—
249C4⋊C4—3021no—
250C4⋊C4—1511no—
251C4⋊C4—1511no—
252C4⋊C4—1511no—
253C4⋊C4—1511no—
254C4⋊C4—1511no—
255C4⋊C4—1511no—
256C4⋊C4D60411yescharacteristic
257C4⋊C4D60411yescharacteristic
258C22⋊C4—3021no—
259C22⋊C4—3021no—
260C22⋊C4—3021no—
261C22⋊C4—3021no—
262C22⋊C4—3021no—
263C22⋊C4D60411yescharacteristic
264C22⋊C4D60411yescharacteristic
265C42—3021no—
266C42C22×D15111yescharacteristic
267C42C22×D15111yescharacteristic
268C23—3021no—
269C23—3021no—
270C23C2×D60411yescharacteristic
271Q8—12081no—
272Q8—12081no—
273D4—3021no—
274D4—3021no—
275D4—3021no—
276D4—3021no—
277D4—12081no—
278D4—12081no—
279D4—12081no—
280D4—12081no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—3021no—
284C2×C4—3021no—
285C2×C4—3021no—
286C2×C4—3021no—
287C2×C4—3021no—
288C2×C4—3021no—
289C2×C4—12081no—
290C2×C4—12081no—
291C2×C4—12081no—
292C2×C4C2×D60411yescharacteristic
293C2×C4C2×D60411yescharacteristic
294C2×C4C2×D60411yescharacteristic
295C2×C4C2×D60411yescharacteristic
296C2×C4C2×D60411yescharacteristic
297C2×C4C23×D15111yescharacteristic
298C8—21no—
299C8—21no—
300C8—21no—
301C8—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—6041no—
306C22—6041no—
307C22—6041no—
308C22—6041no—
309C22—6041no—
310C22—6041no—
311C22C22×D60411yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—6041no—
318C4—6041no—
319C4—6041no—
320C4—6041no—
321C4—6041no—
322C4—6041no—
323C4#1801278611yescharacteristic
324C4#1801278611yescharacteristic
325C2—41no—
326C2—12081no—
327C2—12081no—
328C2#2375278811yescharacteristic
329C2#2375301711yescharacteristic
330C2#2375302411yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
prime radical#23752817C2
hypercenter#433D151
hypocenterC151#3241
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23752840C2semidirect
3. #23752621C2semidirect
4. #23752614C2semidirect
5. #23752577C2semidirect
6. #23752559C2semidirect
7. #23752537C2semidirect
8. #23752537C2semidirect
9. #23752531C2semidirect
10. #23752526C2semidirect
11. #23752513C2semidirect
12. #23752513C2semidirect
13. #23752503C2semidirect
14. #23752493C2semidirect
15. #433×C151C2semidirect
165. C151#3241semidirect
181. #433D151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237528402
#237528172
#237526212
#237526142
#237525772
#237525592
#237525372
#237525312
#237525262
#237525132
#237525032
#237524932
#433×C1512
#3241151